Perfectly matching concentric shell walls?
You can join the two meshes in object mode.  Then in edit mode you you can select the two edge and perform a Bridge Edge Loop.  That will also serve as a check to make sure you have the same number of vertices.

If you want two separate objects. You could start with one hemisphere, [solidify modifier], apply the modifier,  The select the inner portion and menu [separate] to form two separate meshes.